Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded
Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.
library(reportfactory)
library(here)
library(rio)
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)These scripts will load:
.R files inside /scripts/.R files inside /src/These scripts also contain routines to access the latest clean encrypted data (see next section).
We import the latest NHS pathways data:
x <- import_pathways() %>%
as_tibble()
x
## [90m# A tibble: 184,059 x 11[39m
## site_type date sex age ccg_code ccg_name count postcode nhs_region
## [3m[90m<chr>[39m[23m [3m[90m<date>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<int>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m
## [90m 1[39m 111 2020-03-18 fema… miss… e380000… nhs_glo… 1 gl34fe South West
## [90m 2[39m 111 2020-03-18 fema… miss… e380001… nhs_sou… 1 ne325nn North Eas…
## [90m 3[39m 111 2020-03-18 fema… 0-18 e380000… nhs_air… 8 bd57jr North Eas…
## [90m 4[39m 111 2020-03-18 fema… 0-18 e380000… nhs_ash… 7 tn254ab South East
## [90m 5[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 35 rm13ae London
## [90m 6[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 9 n111np London
## [90m 7[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 11 s752py North Eas…
## [90m 8[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bas… 19 ss143hg East of E…
## [90m 9[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bas… 6 dn227xf North Eas…
## [90m10[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bat… 9 ba25rp South West
## [90m# … with 184,049 more rows, and 2 more variables: day [3m[90m<int>[90m[23m, weekday [3m[90m<fct>[90m[23m[39mWe also import demographics data for NHS regions in England, used later in our analysis:
path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
## nhs_region variable value
## 1 North West 0-18 0.22538599
## 2 North East and Yorkshire 0-18 0.21876449
## 3 Midlands 0-18 0.22564656
## 4 East of England 0-18 0.22810783
## 5 London 0-18 0.23764782
## 6 South East 0-18 0.22458811
## 7 South West 0-18 0.20799797
## 8 North West 19-69 0.64274078
## 9 North East and Yorkshire 19-69 0.64437753
## 10 Midlands 19-69 0.63876675
## 11 East of England 19-69 0.63034229
## 12 London 19-69 0.67820084
## 13 South East 19-69 0.63267336
## 14 South West 19-69 0.63176131
## 15 North West 70-120 0.13187323
## 16 North East and Yorkshire 70-120 0.13685797
## 17 Midlands 70-120 0.13558669
## 18 East of England 70-120 0.14154988
## 19 London 70-120 0.08415135
## 20 South East 70-120 0.14273853
## 21 South West 70-120 0.16024072Finally, we import publically available deaths per NHS region:
dth <- import_deaths() %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
#truncation to account for reporting delay
delay_max <- 21
dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
## date_report nhs_region deaths
## 1 2020-03-01 East of England 0
## 2 2020-03-02 East of England 1
## 3 2020-03-03 East of England 0
## 4 2020-03-04 East of England 0
## 5 2020-03-05 East of England 0
## 6 2020-03-06 East of England 1
## 7 2020-03-07 East of England 0
## 8 2020-03-08 East of England 0
## 9 2020-03-09 East of England 1
## 10 2020-03-10 East of England 0
## 11 2020-03-11 East of England 0
## 12 2020-03-12 East of England 0
## 13 2020-03-13 East of England 1
## 14 2020-03-14 East of England 2
## 15 2020-03-15 East of England 2
## 16 2020-03-16 East of England 1
## 17 2020-03-17 East of England 1
## 18 2020-03-18 East of England 5
## 19 2020-03-19 East of England 4
## 20 2020-03-20 East of England 2
## 21 2020-03-21 East of England 11
## 22 2020-03-22 East of England 12
## 23 2020-03-23 East of England 11
## 24 2020-03-24 East of England 19
## 25 2020-03-25 East of England 26
## 26 2020-03-26 East of England 36
## 27 2020-03-27 East of England 38
## 28 2020-03-28 East of England 28
## 29 2020-03-29 East of England 43
## 30 2020-03-30 East of England 45
## 31 2020-03-31 East of England 70
## 32 2020-04-01 East of England 62
## 33 2020-04-02 East of England 65
## 34 2020-04-03 East of England 80
## 35 2020-04-04 East of England 71
## 36 2020-04-05 East of England 76
## 37 2020-04-06 East of England 71
## 38 2020-04-07 East of England 93
## 39 2020-04-08 East of England 111
## 40 2020-04-09 East of England 87
## 41 2020-04-10 East of England 74
## 42 2020-04-11 East of England 92
## 43 2020-04-12 East of England 100
## 44 2020-04-13 East of England 78
## 45 2020-04-14 East of England 61
## 46 2020-04-15 East of England 82
## 47 2020-04-16 East of England 74
## 48 2020-04-17 East of England 86
## 49 2020-04-18 East of England 64
## 50 2020-04-19 East of England 67
## 51 2020-04-20 East of England 67
## 52 2020-04-21 East of England 75
## 53 2020-04-22 East of England 67
## 54 2020-04-23 East of England 49
## 55 2020-04-24 East of England 66
## 56 2020-04-25 East of England 54
## 57 2020-04-26 East of England 48
## 58 2020-04-27 East of England 46
## 59 2020-04-28 East of England 58
## 60 2020-04-29 East of England 32
## 61 2020-04-30 East of England 45
## 62 2020-05-01 East of England 49
## 63 2020-05-02 East of England 29
## 64 2020-05-03 East of England 41
## 65 2020-05-04 East of England 19
## 66 2020-05-05 East of England 36
## 67 2020-05-06 East of England 31
## 68 2020-05-07 East of England 33
## 69 2020-05-08 East of England 33
## 70 2020-05-09 East of England 29
## 71 2020-05-10 East of England 22
## 72 2020-05-11 East of England 18
## 73 2020-05-12 East of England 21
## 74 2020-05-13 East of England 27
## 75 2020-05-14 East of England 26
## 76 2020-05-15 East of England 19
## 77 2020-05-16 East of England 26
## 78 2020-05-17 East of England 17
## 79 2020-05-18 East of England 25
## 80 2020-05-19 East of England 15
## 81 2020-05-20 East of England 26
## 82 2020-05-21 East of England 21
## 83 2020-05-22 East of England 13
## 84 2020-05-23 East of England 12
## 85 2020-05-24 East of England 17
## 86 2020-05-25 East of England 25
## 87 2020-05-26 East of England 14
## 88 2020-05-27 East of England 12
## 89 2020-05-28 East of England 17
## 90 2020-05-29 East of England 16
## 91 2020-05-30 East of England 9
## 92 2020-05-31 East of England 8
## 93 2020-06-01 East of England 17
## 94 2020-06-02 East of England 14
## 95 2020-06-03 East of England 10
## 96 2020-06-04 East of England 7
## 97 2020-06-05 East of England 14
## 98 2020-06-06 East of England 5
## 99 2020-06-07 East of England 9
## 100 2020-06-08 East of England 7
## 101 2020-06-09 East of England 6
## 102 2020-06-10 East of England 8
## 103 2020-06-11 East of England 1
## 104 2020-06-12 East of England 9
## 105 2020-06-13 East of England 5
## 106 2020-06-14 East of England 4
## 107 2020-06-15 East of England 8
## 108 2020-06-16 East of England 3
## 109 2020-06-17 East of England 7
## 110 2020-06-18 East of England 4
## 111 2020-06-19 East of England 7
## 112 2020-06-20 East of England 4
## 113 2020-06-21 East of England 3
## 114 2020-06-22 East of England 6
## 115 2020-06-23 East of England 5
## 116 2020-06-24 East of England 4
## 117 2020-06-25 East of England 1
## 118 2020-06-26 East of England 5
## 119 2020-06-27 East of England 6
## 120 2020-06-28 East of England 8
## 121 2020-06-29 East of England 4
## 122 2020-06-30 East of England 5
## 123 2020-07-01 East of England 2
## 124 2020-07-02 East of England 5
## 125 2020-07-03 East of England 0
## 126 2020-07-04 East of England 3
## 127 2020-07-05 East of England 1
## 128 2020-07-06 East of England 2
## 129 2020-07-07 East of England 2
## 130 2020-07-08 East of England 0
## 131 2020-07-09 East of England 8
## 132 2020-07-10 East of England 4
## 133 2020-07-11 East of England 2
## 134 2020-07-12 East of England 1
## 135 2020-07-13 East of England 7
## 136 2020-07-14 East of England 2
## 137 2020-07-15 East of England 0
## 138 2020-07-16 East of England 0
## 139 2020-07-17 East of England 0
## 140 2020-07-18 East of England 0
## 141 2020-07-19 East of England 1
## 142 2020-07-20 East of England 1
## 143 2020-07-21 East of England 0
## 144 2020-03-01 London 0
## 145 2020-03-02 London 0
## 146 2020-03-03 London 0
## 147 2020-03-04 London 0
## 148 2020-03-05 London 0
## 149 2020-03-06 London 1
## 150 2020-03-07 London 0
## 151 2020-03-08 London 0
## 152 2020-03-09 London 1
## 153 2020-03-10 London 0
## 154 2020-03-11 London 5
## 155 2020-03-12 London 6
## 156 2020-03-13 London 10
## 157 2020-03-14 London 13
## 158 2020-03-15 London 9
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## 160 2020-03-17 London 23
## 161 2020-03-18 London 27
## 162 2020-03-19 London 25
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## 169 2020-03-26 London 129
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## 171 2020-03-28 London 122
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## 175 2020-04-01 London 202
## 176 2020-04-02 London 191
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## 180 2020-04-06 London 197
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## 184 2020-04-10 London 170
## 185 2020-04-11 London 178
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## 191 2020-04-17 London 100
## 192 2020-04-18 London 101
## 193 2020-04-19 London 103
## 194 2020-04-20 London 95
## 195 2020-04-21 London 94
## 196 2020-04-22 London 109
## 197 2020-04-23 London 77
## 198 2020-04-24 London 71
## 199 2020-04-25 London 58
## 200 2020-04-26 London 53
## 201 2020-04-27 London 51
## 202 2020-04-28 London 44
## 203 2020-04-29 London 45
## 204 2020-04-30 London 40
## 205 2020-05-01 London 41
## 206 2020-05-02 London 41
## 207 2020-05-03 London 36
## 208 2020-05-04 London 30
## 209 2020-05-05 London 25
## 210 2020-05-06 London 37
## 211 2020-05-07 London 37
## 212 2020-05-08 London 30
## 213 2020-05-09 London 23
## 214 2020-05-10 London 26
## 215 2020-05-11 London 18
## 216 2020-05-12 London 18
## 217 2020-05-13 London 17
## 218 2020-05-14 London 20
## 219 2020-05-15 London 18
## 220 2020-05-16 London 14
## 221 2020-05-17 London 15
## 222 2020-05-18 London 10
## 223 2020-05-19 London 14
## 224 2020-05-20 London 19
## 225 2020-05-21 London 12
## 226 2020-05-22 London 10
## 227 2020-05-23 London 6
## 228 2020-05-24 London 7
## 229 2020-05-25 London 9
## 230 2020-05-26 London 13
## 231 2020-05-27 London 7
## 232 2020-05-28 London 8
## 233 2020-05-29 London 7
## 234 2020-05-30 London 12
## 235 2020-05-31 London 6
## 236 2020-06-01 London 10
## 237 2020-06-02 London 8
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## 239 2020-06-04 London 8
## 240 2020-06-05 London 4
## 241 2020-06-06 London 0
## 242 2020-06-07 London 5
## 243 2020-06-08 London 5
## 244 2020-06-09 London 4
## 245 2020-06-10 London 7
## 246 2020-06-11 London 5
## 247 2020-06-12 London 3
## 248 2020-06-13 London 3
## 249 2020-06-14 London 3
## 250 2020-06-15 London 1
## 251 2020-06-16 London 2
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## 253 2020-06-18 London 2
## 254 2020-06-19 London 5
## 255 2020-06-20 London 3
## 256 2020-06-21 London 4
## 257 2020-06-22 London 2
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## 260 2020-06-25 London 3
## 261 2020-06-26 London 2
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## 288 2020-03-02 Midlands 0
## 289 2020-03-03 Midlands 1
## 290 2020-03-04 Midlands 0
## 291 2020-03-05 Midlands 0
## 292 2020-03-06 Midlands 0
## 293 2020-03-07 Midlands 0
## 294 2020-03-08 Midlands 2
## 295 2020-03-09 Midlands 1
## 296 2020-03-10 Midlands 0
## 297 2020-03-11 Midlands 2
## 298 2020-03-12 Midlands 6
## 299 2020-03-13 Midlands 5
## 300 2020-03-14 Midlands 4
## 301 2020-03-15 Midlands 5
## 302 2020-03-16 Midlands 11
## 303 2020-03-17 Midlands 8
## 304 2020-03-18 Midlands 13
## 305 2020-03-19 Midlands 8
## 306 2020-03-20 Midlands 28
## 307 2020-03-21 Midlands 13
## 308 2020-03-22 Midlands 31
## 309 2020-03-23 Midlands 33
## 310 2020-03-24 Midlands 41
## 311 2020-03-25 Midlands 48
## 312 2020-03-26 Midlands 64
## 313 2020-03-27 Midlands 72
## 314 2020-03-28 Midlands 89
## 315 2020-03-29 Midlands 92
## 316 2020-03-30 Midlands 90
## 317 2020-03-31 Midlands 123
## 318 2020-04-01 Midlands 140
## 319 2020-04-02 Midlands 142
## 320 2020-04-03 Midlands 124
## 321 2020-04-04 Midlands 151
## 322 2020-04-05 Midlands 164
## 323 2020-04-06 Midlands 140
## 324 2020-04-07 Midlands 123
## 325 2020-04-08 Midlands 186
## 326 2020-04-09 Midlands 139
## 327 2020-04-10 Midlands 127
## 328 2020-04-11 Midlands 142
## 329 2020-04-12 Midlands 139
## 330 2020-04-13 Midlands 120
## 331 2020-04-14 Midlands 116
## 332 2020-04-15 Midlands 147
## 333 2020-04-16 Midlands 102
## 334 2020-04-17 Midlands 118
## 335 2020-04-18 Midlands 115
## 336 2020-04-19 Midlands 92
## 337 2020-04-20 Midlands 107
## 338 2020-04-21 Midlands 86
## 339 2020-04-22 Midlands 78
## 340 2020-04-23 Midlands 103
## 341 2020-04-24 Midlands 79
## 342 2020-04-25 Midlands 72
## 343 2020-04-26 Midlands 81
## 344 2020-04-27 Midlands 74
## 345 2020-04-28 Midlands 68
## 346 2020-04-29 Midlands 53
## 347 2020-04-30 Midlands 56
## 348 2020-05-01 Midlands 64
## 349 2020-05-02 Midlands 51
## 350 2020-05-03 Midlands 52
## 351 2020-05-04 Midlands 61
## 352 2020-05-05 Midlands 59
## 353 2020-05-06 Midlands 59
## 354 2020-05-07 Midlands 48
## 355 2020-05-08 Midlands 34
## 356 2020-05-09 Midlands 37
## 357 2020-05-10 Midlands 42
## 358 2020-05-11 Midlands 33
## 359 2020-05-12 Midlands 45
## 360 2020-05-13 Midlands 40
## 361 2020-05-14 Midlands 38
## 362 2020-05-15 Midlands 40
## 363 2020-05-16 Midlands 34
## 364 2020-05-17 Midlands 31
## 365 2020-05-18 Midlands 36
## 366 2020-05-19 Midlands 35
## 367 2020-05-20 Midlands 36
## 368 2020-05-21 Midlands 32
## 369 2020-05-22 Midlands 27
## 370 2020-05-23 Midlands 34
## 371 2020-05-24 Midlands 20
## 372 2020-05-25 Midlands 26
## 373 2020-05-26 Midlands 33
## 374 2020-05-27 Midlands 29
## 375 2020-05-28 Midlands 28
## 376 2020-05-29 Midlands 20
## 377 2020-05-30 Midlands 21
## 378 2020-05-31 Midlands 22
## 379 2020-06-01 Midlands 20
## 380 2020-06-02 Midlands 22
## 381 2020-06-03 Midlands 24
## 382 2020-06-04 Midlands 16
## 383 2020-06-05 Midlands 21
## 384 2020-06-06 Midlands 20
## 385 2020-06-07 Midlands 17
## 386 2020-06-08 Midlands 16
## 387 2020-06-09 Midlands 18
## 388 2020-06-10 Midlands 15
## 389 2020-06-11 Midlands 13
## 390 2020-06-12 Midlands 12
## 391 2020-06-13 Midlands 6
## 392 2020-06-14 Midlands 18
## 393 2020-06-15 Midlands 12
## 394 2020-06-16 Midlands 15
## 395 2020-06-17 Midlands 11
## 396 2020-06-18 Midlands 15
## 397 2020-06-19 Midlands 10
## 398 2020-06-20 Midlands 15
## 399 2020-06-21 Midlands 14
## 400 2020-06-22 Midlands 14
## 401 2020-06-23 Midlands 16
## 402 2020-06-24 Midlands 15
## 403 2020-06-25 Midlands 18
## 404 2020-06-26 Midlands 5
## 405 2020-06-27 Midlands 5
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## 407 2020-06-29 Midlands 6
## 408 2020-06-30 Midlands 6
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## 412 2020-07-04 Midlands 4
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## 414 2020-07-06 Midlands 5
## 415 2020-07-07 Midlands 3
## 416 2020-07-08 Midlands 5
## 417 2020-07-09 Midlands 8
## 418 2020-07-10 Midlands 3
## 419 2020-07-11 Midlands 0
## 420 2020-07-12 Midlands 5
## 421 2020-07-13 Midlands 1
## 422 2020-07-14 Midlands 1
## 423 2020-07-15 Midlands 6
## 424 2020-07-16 Midlands 2
## 425 2020-07-17 Midlands 1
## 426 2020-07-18 Midlands 2
## 427 2020-07-19 Midlands 2
## 428 2020-07-20 Midlands 0
## 429 2020-07-21 Midlands 0
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## 431 2020-03-02 North East and Yorkshire 0
## 432 2020-03-03 North East and Yorkshire 0
## 433 2020-03-04 North East and Yorkshire 0
## 434 2020-03-05 North East and Yorkshire 0
## 435 2020-03-06 North East and Yorkshire 0
## 436 2020-03-07 North East and Yorkshire 0
## 437 2020-03-08 North East and Yorkshire 0
## 438 2020-03-09 North East and Yorkshire 0
## 439 2020-03-10 North East and Yorkshire 0
## 440 2020-03-11 North East and Yorkshire 0
## 441 2020-03-12 North East and Yorkshire 0
## 442 2020-03-13 North East and Yorkshire 0
## 443 2020-03-14 North East and Yorkshire 0
## 444 2020-03-15 North East and Yorkshire 2
## 445 2020-03-16 North East and Yorkshire 3
## 446 2020-03-17 North East and Yorkshire 1
## 447 2020-03-18 North East and Yorkshire 2
## 448 2020-03-19 North East and Yorkshire 6
## 449 2020-03-20 North East and Yorkshire 5
## 450 2020-03-21 North East and Yorkshire 6
## 451 2020-03-22 North East and Yorkshire 7
## 452 2020-03-23 North East and Yorkshire 9
## 453 2020-03-24 North East and Yorkshire 8
## 454 2020-03-25 North East and Yorkshire 18
## 455 2020-03-26 North East and Yorkshire 21
## 456 2020-03-27 North East and Yorkshire 28
## 457 2020-03-28 North East and Yorkshire 35
## 458 2020-03-29 North East and Yorkshire 38
## 459 2020-03-30 North East and Yorkshire 64
## 460 2020-03-31 North East and Yorkshire 60
## 461 2020-04-01 North East and Yorkshire 67
## 462 2020-04-02 North East and Yorkshire 75
## 463 2020-04-03 North East and Yorkshire 100
## 464 2020-04-04 North East and Yorkshire 105
## 465 2020-04-05 North East and Yorkshire 92
## 466 2020-04-06 North East and Yorkshire 96
## 467 2020-04-07 North East and Yorkshire 102
## 468 2020-04-08 North East and Yorkshire 107
## 469 2020-04-09 North East and Yorkshire 111
## 470 2020-04-10 North East and Yorkshire 117
## 471 2020-04-11 North East and Yorkshire 98
## 472 2020-04-12 North East and Yorkshire 84
## 473 2020-04-13 North East and Yorkshire 94
## 474 2020-04-14 North East and Yorkshire 107
## 475 2020-04-15 North East and Yorkshire 96
## 476 2020-04-16 North East and Yorkshire 103
## 477 2020-04-17 North East and Yorkshire 88
## 478 2020-04-18 North East and Yorkshire 95
## 479 2020-04-19 North East and Yorkshire 88
## 480 2020-04-20 North East and Yorkshire 100
## 481 2020-04-21 North East and Yorkshire 76
## 482 2020-04-22 North East and Yorkshire 84
## 483 2020-04-23 North East and Yorkshire 63
## 484 2020-04-24 North East and Yorkshire 72
## 485 2020-04-25 North East and Yorkshire 69
## 486 2020-04-26 North East and Yorkshire 65
## 487 2020-04-27 North East and Yorkshire 65
## 488 2020-04-28 North East and Yorkshire 57
## 489 2020-04-29 North East and Yorkshire 69
## 490 2020-04-30 North East and Yorkshire 57
## 491 2020-05-01 North East and Yorkshire 64
## 492 2020-05-02 North East and Yorkshire 48
## 493 2020-05-03 North East and Yorkshire 40
## 494 2020-05-04 North East and Yorkshire 49
## 495 2020-05-05 North East and Yorkshire 40
## 496 2020-05-06 North East and Yorkshire 51
## 497 2020-05-07 North East and Yorkshire 45
## 498 2020-05-08 North East and Yorkshire 42
## 499 2020-05-09 North East and Yorkshire 44
## 500 2020-05-10 North East and Yorkshire 40
## 501 2020-05-11 North East and Yorkshire 29
## 502 2020-05-12 North East and Yorkshire 27
## 503 2020-05-13 North East and Yorkshire 28
## 504 2020-05-14 North East and Yorkshire 31
## 505 2020-05-15 North East and Yorkshire 32
## 506 2020-05-16 North East and Yorkshire 35
## 507 2020-05-17 North East and Yorkshire 26
## 508 2020-05-18 North East and Yorkshire 30
## 509 2020-05-19 North East and Yorkshire 27
## 510 2020-05-20 North East and Yorkshire 22
## 511 2020-05-21 North East and Yorkshire 33
## 512 2020-05-22 North East and Yorkshire 22
## 513 2020-05-23 North East and Yorkshire 18
## 514 2020-05-24 North East and Yorkshire 26
## 515 2020-05-25 North East and Yorkshire 21
## 516 2020-05-26 North East and Yorkshire 21
## 517 2020-05-27 North East and Yorkshire 22
## 518 2020-05-28 North East and Yorkshire 21
## 519 2020-05-29 North East and Yorkshire 25
## 520 2020-05-30 North East and Yorkshire 20
## 521 2020-05-31 North East and Yorkshire 20
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## 523 2020-06-02 North East and Yorkshire 23
## 524 2020-06-03 North East and Yorkshire 23
## 525 2020-06-04 North East and Yorkshire 17
## 526 2020-06-05 North East and Yorkshire 18
## 527 2020-06-06 North East and Yorkshire 21
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## 530 2020-06-09 North East and Yorkshire 12
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## 534 2020-06-13 North East and Yorkshire 10
## 535 2020-06-14 North East and Yorkshire 11
## 536 2020-06-15 North East and Yorkshire 9
## 537 2020-06-16 North East and Yorkshire 10
## 538 2020-06-17 North East and Yorkshire 9
## 539 2020-06-18 North East and Yorkshire 11
## 540 2020-06-19 North East and Yorkshire 6
## 541 2020-06-20 North East and Yorkshire 5
## 542 2020-06-21 North East and Yorkshire 4
## 543 2020-06-22 North East and Yorkshire 6
## 544 2020-06-23 North East and Yorkshire 7
## 545 2020-06-24 North East and Yorkshire 10
## 546 2020-06-25 North East and Yorkshire 4
## 547 2020-06-26 North East and Yorkshire 7
## 548 2020-06-27 North East and Yorkshire 3
## 549 2020-06-28 North East and Yorkshire 5
## 550 2020-06-29 North East and Yorkshire 2
## 551 2020-06-30 North East and Yorkshire 5
## 552 2020-07-01 North East and Yorkshire 1
## 553 2020-07-02 North East and Yorkshire 4
## 554 2020-07-03 North East and Yorkshire 3
## 555 2020-07-04 North East and Yorkshire 4
## 556 2020-07-05 North East and Yorkshire 2
## 557 2020-07-06 North East and Yorkshire 2
## 558 2020-07-07 North East and Yorkshire 3
## 559 2020-07-08 North East and Yorkshire 3
## 560 2020-07-09 North East and Yorkshire 0
## 561 2020-07-10 North East and Yorkshire 3
## 562 2020-07-11 North East and Yorkshire 1
## 563 2020-07-12 North East and Yorkshire 4
## 564 2020-07-13 North East and Yorkshire 1
## 565 2020-07-14 North East and Yorkshire 1
## 566 2020-07-15 North East and Yorkshire 2
## 567 2020-07-16 North East and Yorkshire 2
## 568 2020-07-17 North East and Yorkshire 1
## 569 2020-07-18 North East and Yorkshire 2
## 570 2020-07-19 North East and Yorkshire 2
## 571 2020-07-20 North East and Yorkshire 1
## 572 2020-07-21 North East and Yorkshire 0
## 573 2020-03-01 North West 0
## 574 2020-03-02 North West 0
## 575 2020-03-03 North West 0
## 576 2020-03-04 North West 0
## 577 2020-03-05 North West 1
## 578 2020-03-06 North West 0
## 579 2020-03-07 North West 0
## 580 2020-03-08 North West 1
## 581 2020-03-09 North West 0
## 582 2020-03-10 North West 0
## 583 2020-03-11 North West 0
## 584 2020-03-12 North West 2
## 585 2020-03-13 North West 3
## 586 2020-03-14 North West 1
## 587 2020-03-15 North West 4
## 588 2020-03-16 North West 2
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## 597 2020-03-25 North West 21
## 598 2020-03-26 North West 29
## 599 2020-03-27 North West 36
## 600 2020-03-28 North West 28
## 601 2020-03-29 North West 46
## 602 2020-03-30 North West 67
## 603 2020-03-31 North West 52
## 604 2020-04-01 North West 86
## 605 2020-04-02 North West 96
## 606 2020-04-03 North West 95
## 607 2020-04-04 North West 98
## 608 2020-04-05 North West 102
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## 706 2020-07-12 North West 0
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## 853 2020-07-16 South East 3
## 854 2020-07-17 South East 1
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## 857 2020-07-20 South East 1
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## 939 2020-05-20 South West 1
## 940 2020-05-21 South West 9
## 941 2020-05-22 South West 6
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## 943 2020-05-24 South West 3
## 944 2020-05-25 South West 8
## 945 2020-05-26 South West 11
## 946 2020-05-27 South West 5
## 947 2020-05-28 South West 10
## 948 2020-05-29 South West 7
## 949 2020-05-30 South West 3
## 950 2020-05-31 South West 2
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## 959 2020-06-09 South West 0
## 960 2020-06-10 South West 1
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## 967 2020-06-17 South West 0
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## 975 2020-06-25 South West 0
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## 977 2020-06-27 South West 0
## 978 2020-06-28 South West 0
## 979 2020-06-29 South West 1
## 980 2020-06-30 South West 0
## 981 2020-07-01 South West 0
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## 985 2020-07-05 South West 1
## 986 2020-07-06 South West 0
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## 988 2020-07-08 South West 2
## 989 2020-07-09 South West 0
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## 993 2020-07-13 South West 1
## 994 2020-07-14 South West 0
## 995 2020-07-15 South West 0
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## 997 2020-07-17 South West 1
## 998 2020-07-18 South West 0
## 999 2020-07-19 South West 0
## 1000 2020-07-20 South West 0
## 1001 2020-07-21 South West 0We extract the completion date from the NHS Pathways file timestamp:
The completion date of the NHS Pathways data is Tuesday 21 Jul 2020.
These are functions which will be used further in the analyses.
Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:
## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here
Rsq <- function(x) {
1 - (x$deviance / x$null.deviance)
}Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:
## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals
get_r <- function(model) {
## extract coefficients and conf int
out <- data.frame(r = coef(model)) %>%
rownames_to_column("var") %>%
cbind(confint(model)) %>%
filter(!grepl("day_of_week", var)) %>%
filter(grepl("day", var)) %>%
rename(lower_95 = "2.5 %",
upper_95 = "97.5 %") %>%
mutate(var = sub("day:", "", var))
## reconstruct values: intercept + region-coefficient
for (i in 2:nrow(out)) {
out[i, -1] <- out[1, -1] + out[i, -1]
}
## find the name of the intercept, restore regions names
out <- out %>%
mutate(nhs_region = model$xlevels$nhs_region) %>%
select(nhs_region, everything(), -var)
## find halving times
halving <- log(0.5) / out[,-1] %>%
rename(halving_t = r,
halving_t_lower_95 = lower_95,
halving_t_upper_95 = upper_95)
## set halving times with exclusion intervals to NA
no_halving <- out$lower_95 < 0 & out$upper_95 > 0
halving[no_halving, ] <- NA_real_
## return all data
cbind(out, halving)
}Functions used in the correlation analysis between NHS Pathways reports and deaths:
## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.
getcor <- function(x, ndx) {
return(cor(x$deaths[ndx],
x$note_lag[ndx],
use = "complete.obs",
method = "pearson"))
}
## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)
getboot <- function(x) {
result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000),
type = "bca")
return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
r = result$t0,
r_low = result$bca[4],
r_hi = result$bca[5]))
}Function to classify the day of the week into weekend, Monday, and the rest:
## Fn to add day of week
day_of_week <- function(df) {
df %>%
dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>%
dplyr::mutate(day_of_week = dplyr::case_when(
day_of_week %in% c("Sat", "Sun") ~ "weekend",
day_of_week %in% c("Mon") ~ "monday",
!(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
) %>%
factor(levels = c("rest_of_week", "monday", "weekend")))
}Custom color palettes, color scales, and vectors of colors:
We look for temporal patterns in COVID-19 related 111/999 calls and 111 online reports. Analyses are broken down by NHS region. We also look for estimates of recent growth rate and associated doubling / halving time.
tab_date_region_all <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
dth %>%
mutate(trusted = case_when(date_report < max(dth$date_report)-delay_max ~ "Y",
date_report >= max(dth$date_report)-delay_max ~ "N"),
value = "Deaths",
vline = max(dth$date_report)-delay_max-1,
lab = "Truncated for reporting delay",
lab_pos_x = vline + 10,
lab_pos_y = 150,
lab_col = "darkgrey") %>%
rename(date = date_report,
n = deaths) %>%
bind_rows(
mutate(tab_date_region_all, value = "Reports",
trusted = "Y",
vline = as.Date("2020-03-23"),
lab = "Start of UK lockdown",
lab_pos_x = vline - 8,
lab_pos_y = 30200,
lab_col = "black")
) %>%
mutate(value = factor(value, levels = c("Reports","Deaths"))) -> dths_reports
plot_dth_report <-
ggplot(dths_reports, aes(date, n, colour = nhs_region)) +
# Add main points and lines, coloured by region and fade out deaths for excluded period
geom_point(aes(alpha = trusted)) +
geom_line(alpha = 0.2) +
geom_smooth(method = "loess", span = .5, color = "black") +
scale_colour_manual("", values = pal) +
scale_alpha_manual(values = c(0.3,1)) +
guides(alpha = F) +
# Add vertical markers for important dates with labels - different for each facet
ggnewscale::new_scale_colour() +
geom_vline(aes(xintercept = vline, col = value), lty = "solid") +
geom_text(aes(x = lab_pos_x, y = lab_pos_y, label = lab, col = value), size = 3) +
scale_colour_manual("",values = c("black","darkgrey"), guide = F) +
# Facet by deaths and reports
facet_grid(rows = vars(value), scales = "free_y", switch = "y") +
# Other formatting
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",strip.placement = "outside") +
rotate_x +
labs(x = NULL,
y = NULL)
plot_dth_reportWe plot the number of 111/999 calls and 111 online reports by age, and the proportion of 111/999 calls and 111 online reports by age. In the second graph, the vertical lines indicate the proportion of individuals residing in the corresponding NHS region who belong to the corresponding age group.
tab_date_region_age_all <- x %>%
filter(!is.na(nhs_region),
age != "missing") %>%
group_by(date, nhs_region, age) %>%
summarise(n = sum(count))
tab_date_region_age_all %>%
ggplot(aes(x = date, y = n, fill = age)) +
geom_col(position = "stack") +
scale_fill_manual(values = age.pal) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(fill = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Total daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
tab_date_region_age_all <- tab_date_region_age_all %>%
group_by(date, nhs_region) %>%
summarise(tot = sum(n)) %>%
left_join(tab_date_region_age_all, by = c("date", "nhs_region")) %>%
mutate(prop_n = n/tot)
tab_date_region_age_all %>%
ggplot(aes(x = date, y = prop_n, color = age)) +
scale_color_manual(values = age.pal) +
geom_line() +
geom_point() +
geom_hline(data = nhs_region_pop, aes(yintercept = value, color = variable)) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(color = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Proportion of daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)We fit quasi-Poisson GLMs for 14-day windows to get growth rates over time.
## set moving time window (1/2/3 weeks)
w <- 14
# create empty df
r_all_sliding <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding <- bind_rows(r_all_sliding, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding <- r_all_sliding %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))We examine the evolution of the growth rate by region over time.
# plot
plot_growth <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)From the growth rate, we derive R and examine its value through time.
# plot
plot_R <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
rotate_x +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
# strip.text.x = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "",
override.aes = list(fill = NA)),
fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))We repeat the above analysis, where we fit quasi-Poisson GLMs for 14-day windows to get growth rates over time, but apply this to each age group separately (0-18, 19-69, 70-120 years old).
We first run the analysis for 0-18 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_0_18 <- NULL
## make data for model
x_model_all_moving_0_18 <- x %>%
filter(!is.na(nhs_region),
age == "0-18") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_0_18$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_0_18 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_0_18 <- bind_rows(r_all_sliding_0_18, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_0_18 <- r_all_sliding_0_18 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_0_18 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_0_18 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_0_18 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then, we run the analysis for 19-69 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_19_69 <- NULL
## make data for model
x_model_all_moving_19_69 <- x %>%
filter(!is.na(nhs_region),
age == "19-69") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_19_69$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_19_69 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_19_69 <- bind_rows(r_all_sliding_19_69, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_19_69 <- r_all_sliding_19_69 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_19_69 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_19_69 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_19_69 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Finally, we run the analysis for 70-120 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_70_120 <- NULL
## make data for model
x_model_all_moving_70_120 <- x %>%
filter(!is.na(nhs_region),
age == "70-120") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_70_120$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_70_120 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_70_120 <- bind_rows(r_all_sliding_70_120, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_70_120 <- r_all_sliding_70_120 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_70_120 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_70_120 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_70_120 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)"))) We combine the estimated growth rates and effective reproduction numbers into a single figure.
ggpubr::ggarrange(fig2_3_0_18,
fig2_3_19_69,
fig2_3_70_120,
nrow = 3,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom",
align = "hv") We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.
Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.
We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.
First we join the NHS Pathways and death data, and aggregate over all England:
## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max
dth_trunc <- dth %>%
rename(date = date_report) %>%
filter(date <= trunc_date)
## join with notification data
all_data <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(count = sum(count, na.rm = T)) %>%
ungroup %>%
inner_join(dth_trunc,
by = c("date","nhs_region"))
all_tot <- all_data %>%
group_by(date) %>%
summarise(count = sum(count, na.rm = TRUE),
deaths = sum(deaths, na.rm = TRUE)) We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:
## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
## lag reports
summary <- all_tot %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI
getboot(.) %>%
mutate(lag = i)
lag_cor <- bind_rows(lag_cor, summary)
}
cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
theme_bw() +
geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_point() +
geom_line() +
labs(x = "Lag between NHS pathways and death data (days)",
y = "Pearson's correlation") +
large_txt
cor_vs_lagThis analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.
all_tot <- all_tot %>%
rename(date_death = date) %>%
mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
date_note = lag(date_death,16))
lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")
summary(lag_mod)
##
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -13.9890 -4.9327 -0.4463 3.8564 8.8587
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.533e+00 6.685e-02 67.81 <2e-16 ***
## note_lag 1.505e-05 6.973e-07 21.58 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 26.75576)
##
## Null deviance: 13578.2 on 81 degrees of freedom
## Residual deviance: 2271.7 on 80 degrees of freedom
## (23 observations deleted due to missingness)
## AIC: NA
##
## Number of Fisher Scoring iterations: 4
exp(coefficients(lag_mod))
## (Intercept) note_lag
## 93.066621 1.000015
exp(confint(lag_mod))
## 2.5 % 97.5 %
## (Intercept) 81.460209 105.871939
## note_lag 1.000014 1.000016
Rsq(lag_mod)
## [1] 0.8326988
mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])
all_tot_pred <-
all_tot %>%
filter(!is.na(note_lag)) %>%
mutate(pred = mod_fit$fit,
pred.se = mod_fit$se.fit,
low = exp(pred - 1.96*pred.se),
hi = exp(pred + 1.96*pred.se))
glm_fit <- all_tot_pred %>%
filter(!is.na(note_lag)) %>%
ggplot(aes(x = note_lag, y = deaths)) +
geom_point() +
geom_line(aes(y = exp(pred))) +
geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
theme_bw() +
labs(y = "Daily number of\ndeaths reported",
x = "Daily number of NHS Pathways reports") +
large_txt
glm_fitThis is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.
SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
meanlog = log(4.7),
sdlog = log(2.9), w = 0.5)
SI_dist1 <- data.frame(x = SI_distribution$r(1e5))
SI_dist1 <- count(SI_dist1, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 30, 5)) +
theme_bw()
SI_dist2 <- data.frame(x = SI_distribution2$r(1e5))
SI_dist2 <- count(SI_dist2, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
theme_bw()
ggpubr::ggarrange(SI_dist1,
SI_dist2,
nrow = 1,
labels = "AUTO") We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.
First with the 7 days window:
## set moving time window (1/2/3 weeks)
w <- 7
# create empty df
r_all_sliding_7days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)plot_R <- r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_7days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_7days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_7 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then with the 21 days window:
## set moving time window (1/2/3 weeks)
w <- 21
# create empty df
r_all_sliding_21days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_21days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_21days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_21 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))And we combine both outputs into a single plot:
ggpubr::ggarrange(r_R_7,
r_R_21,
nrow = 2,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom")
lag_cor_reg <- data.frame()
for (i in 0:30) {
summary <-
all_data %>%
group_by(nhs_region) %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI for each region
group_modify(~getboot(.x)) %>%
mutate(lag = i)
lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}
cor_vs_lag_reg <-
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
geom_point() +
geom_line() +
facet_wrap(~nhs_region) +
scale_color_manual(values = pal) +
scale_fill_manual(values = pal, guide = F) +
theme_bw() +
labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
theme(legend.position = "bottom") +
guides(color = guide_legend(override.aes = list(fill = NA)))
cor_vs_lag_regWe save the tables created during our analysis:
if (!dir.exists("excel_tables")) {
dir.create("excel_tables")
}
## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")
for (e in tables_to_export) {
rio::export(get(e),
file.path("excel_tables",
paste0(e, ".xlsx")))
}
## also export result from regression on lagged data
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))The following information documents the system on which the document was compiled.
This provides information on the operating system.
This provides information on the version of R used:
This provides information on the packages used:
sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.5
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggnewscale_0.4.1 ggpubr_0.4.0 lubridate_1.7.9
## [4] chngpt_2020.5-21 cyphr_1.1.0 DT_0.14
## [7] kableExtra_1.1.0 janitor_2.0.1 remotes_2.2.0
## [10] projections_0.5.1 earlyR_0.0.1 epitrix_0.2.2
## [13] distcrete_1.0.3 incidence_1.7.1 rio_0.5.16
## [16] reshape2_1.4.4 rvest_0.3.5 xml2_1.3.2
## [19] linelist_0.0.40.9000 forcats_0.5.0 stringr_1.4.0
## [22] dplyr_1.0.0 purrr_0.3.4 readr_1.3.1
## [25] tidyr_1.1.0 tibble_3.0.3 ggplot2_3.3.2
## [28] tidyverse_1.3.0 here_0.1 reportfactory_0.0.5
##
## loaded via a namespace (and not attached):
## [1] nlme_3.1-148 fs_1.4.2 webshot_0.5.2 httr_1.4.2
## [5] rprojroot_1.3-2 tools_4.0.2 backports_1.1.8 utf8_1.1.4
## [9] R6_2.4.1 mgcv_1.8-31 DBI_1.1.0 colorspace_1.4-1
## [13] withr_2.2.0 gridExtra_2.3 tidyselect_1.1.0 sodium_1.1
## [17] curl_4.3 compiler_4.0.2 cli_2.0.2 labeling_0.3
## [21] matchmaker_0.1.1 scales_1.1.1 digest_0.6.25 foreign_0.8-80
## [25] rmarkdown_2.3 pkgconfig_2.0.3 htmltools_0.5.0 dbplyr_1.4.4
## [29] htmlwidgets_1.5.1 rlang_0.4.7 readxl_1.3.1 rstudioapi_0.11
## [33] farver_2.0.3 generics_0.0.2 jsonlite_1.7.0 crosstalk_1.1.0.1
## [37] car_3.0-8 zip_2.0.4 magrittr_1.5 kyotil_2019.11-22
## [41] Matrix_1.2-18 Rcpp_1.0.5 munsell_0.5.0 fansi_0.4.1
## [45] viridis_0.5.1 abind_1.4-5 lifecycle_0.2.0 stringi_1.4.6
## [49] yaml_2.2.1 carData_3.0-4 snakecase_0.11.0 MASS_7.3-51.6
## [53] plyr_1.8.6 grid_4.0.2 blob_1.2.1 crayon_1.3.4
## [57] lattice_0.20-41 cowplot_1.0.0 splines_4.0.2 haven_2.3.1
## [61] hms_0.5.3 knitr_1.29 pillar_1.4.6 boot_1.3-25
## [65] ggsignif_0.6.0 reprex_0.3.0 glue_1.4.1 evaluate_0.14
## [69] data.table_1.12.8 modelr_0.1.8 vctrs_0.3.2 selectr_0.4-2
## [73] cellranger_1.1.0 gtable_0.3.0 assertthat_0.2.1 xfun_0.15
## [77] openxlsx_4.1.5 broom_0.7.0 rstatix_0.6.0 survival_3.1-12
## [81] viridisLite_0.3.0 ellipsis_0.3.1